Study On Natural Gradient Based Fast-ICA Algorithm

Blind source separation refers to a process that the source signal is identified or recovered only by observed signals under the condition that unknown characteristics of the transmission channel and any prior knowledge of the source signal. The technique of BSS has a good applications in many fields of signal processing, such as multi-user communications, biomedical engineering, communications array signal processing and image processing. In this dissertation, the blind signal separation algorithms are discussed. This paper focus on the natural gradient based fast-ICA algorithm and the work included are summarized as follows:1. The basic theory and mathod of the BSS problem is systematically addressed. The BSS model is given, we analyze the assumptions of the BSS problem and the two uncertainties for achieving BSS. The contrast function theory is investigated and several typical contrast functions and algorithms are summarized. According to the performance indexes of the algirithms, several typical algorithms are conducted in the simulations.2. The fast-ICA algorithm which is obtained by maximizing the non-Gauss is introduced in detail. It is a two-step algorithm. The observed data is pre-whitened in the first step, the pre-whitening process of the fast-ICA algorithm eliminates the correlation between data effectively and the problem is transformed to seek an orthogonal matrix in the second step. But preliminary whitening will produce error and the pre-whitening error is usually inevitable, the error will accumulate to seek an orthogonal matrix process and affect the convergence and performance of the algorithm. The weight orthogonal constraint of the separating matrix is introduced and the derivation process of the fast-ICA algorithm without pre-whitening proposed by Hyvarinen is achieved.3. The stochastic gradient method is a most popular learning method in the framework of the general nonlinear optimization. However, the parameter space is not Euclidean but has a Riemannian metric space in many cases, such as the perception space of neural learning, the matrix space of blind source separation, linear dynamic systems space of blind deconvolution. In the BSS model, the mixing matrix is unknown so that the parameter space is the space of matrices. Thus the parameter space of BSS has theRiemannian metric structure. Amari has demonstrated that the natural gradient denotes the steepest descent direction of a loss function in the Riemannian space. By using weighted orthogonal constraint and natural gradient, a novel natural gradient based fast-ICA algorithm without pre-whitening is obtained. Simulation results show that the algorithm can effectively separate and reconstruct the source signals and has a faster convergence speed and a better stability compared with fast-ICA.